The Lax-Wendroff method [1]} has been applied to a variety of problems due to its ability in preserving the dispersion relation indirectly for standard compact finite differencing techniques [2]}. Compact analogs of the Lax-Wendroff method were developed [2]}, offering fourth-order accuracy in solving the 1D convection equation. It has also been employed as a correction for wave propagation in attenuating and dispersive media [4]}. The method has been used for treating boundaries for compact schemes [5]}, [6]}. The authors in [7]} implement a Lax-Wendroff type procedure to solve hyperbolic equations that allows one to compute time derivatives recursively by using high-order centered differentiation formulae in the Taylor series expansion in time. The same approach has been used in Lax-Wendroff methods for solving hyperbolic PDEs [8]}. We have explored the properties and numerical performance of the Lax-Wendroff method for sixth order compact scheme of Lele [9]} for uniform grids and the sixth order NUC6 scheme [10]} for non-uniform grids and quantified the resolution for DNS and LES with prescribed tolerance. A thorough analysis of the resulting numerical schemes is performed using GSA. An estimate of the numerical parameters to be chosen to ensure that spatio-temporal scales are resolved to the accuracy desired in performing DNS and LES is given. This has not been attempted before and will serve as a useful tool for practitioners of HPC.
